If the Higgs mass is in a certain range, the quartic self-coupling of the Higgs field becomes negative after renormalization group flow to a high energy scale, signalling an instability of the vacuum itself.
However, I don't know how to interpret the fact that the vacuum appears to be stable at a certain scale, and not stable at a higher scale. Does it mean the actual collapse of the vacuum will start from the higher momentum modes? In other words, when the vacuum collapses, is it true that the value of the scalar field averaged over large distances remain bounded for an extended period of time, but appears to be diverging quickly when averaged over short distances? Also, is it true that such a collapse only happens via the slow process of quantum tunneling under usual circumstances, but will take place quickly if a particle is produced at a high energy comparable to instability energy scale?
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